The presence of anomalous information in a business process event log, such as missing, duplicated or swapped events, hampers the possibility of extracting useful insights from event log analysis. A number of approaches exist in the literature to detect anomalous cases in event logs based on different paradigms, such as probabilistic, distance-based or reconstruction-based anomaly detection. This paper proposes a novel method for anomaly detection in event logs based on the information-theoretic paradigm, which has not been considered before in event log anomaly detection. In particular, we propose an anomaly score for cases of a process based on statistical leverage and three different methods to set the anomaly detection threshold. The proposed approach does not require large data sets to train machine learning models, which are necessary for instance in reconstruction-based approaches. The proposed approach shows remarkable anomaly detection capability in experiments conducted using publicly available event logs in respect of existing methods in the literature. One of the proposed anomaly detection thresholds also shows to handle variable case anomaly ratios more effectively than other methods in the literature.